Summary

This project seeks to improve on the Howard et al. (2020) methods used to estimate sport fish harvest and releases of rockfish in Alaska waters and expand the time series back to 1977 when the statewide harvest survey (SWHS) was first implemented. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and replaces the Howard decision tree approach to low sample sizes with a hierarchical model. The methods and results for generating harvest estimates are generally consistent between the Bayesian model and the Howard methods. Harvest estimates are consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data.

The Bayesian methods depart from the Howard method in how releases are estimated. The Howard methods assume that the species composition of the harvests are equal to the species composition of released fish, which is clearly contraindicated in the logbook data. For instance, logbook data demonstrates that yelloweye have been retained at high levels up until restrictions were enacted in recent years, whereas pelagic rockfish were released in significant numbers in the past with retention increasing in recent years as they have become more prized by anglers. Recent prohibition on retaining yelloweye in Southeast Alaska highlights the the shortcomings of the original Howard methods as the species composition of the harvest would indicate that no yelloweye were caught and released during the closure.

The Howard method for estimating releases for private anglers also relied on an expansion of the logbook release estimates based on the ratio of private:guided releases of all rockfish in the SWHS. In addition to the faulty assumptions about species composition, this method ignores potential bias in SWHS estimates of harvests and releases. As demonstrated below, the bias in those two quantities appears to be quite different based on the logbook data. The Bayesian model thus attempts to estimate release probabilities based on the logbook data coupled with bias corrected estimates from the SWHS.

Lastly, the Howard methods were only used on data beginning in 1999 with the advent of the logbook program and estimates of harvests and releases prior to that have been based on linear ramps from 1999 back to the perceived start of the fishery. The Bayesian methods allow us to expand the time series back to 1977 when the SWHS was implemented by leveraging regional data trends in species composition and the proportion of caught rockfish harvested by species and/or species complex. Key advantages of the Bayesian approach are highlighted in table 1.

Table 1. Summary of key improvements in reconstructiing sport fish removals of rockfish using the Bayesian model as compared to the Howard et al. (2020) methods.
Issue Howard Bayes
Time series 1999 - present 1977 - present
Bias in SWHS Not explicitly dealt with. Relies on logbook data and ratios of guided/unguided from SWHS data to estimate unguided releases and harvests. Explicitly estimates bias in SWHS harvest and release estimates based on logbook data.
Species composition of releases Assumes that species composition of releases is equal to that of the harvest, which is not evident in the logbook data. Recognizes different release probabilities by species / species assemblage and estimates it from logbook data and bias corrected SWHS data
Sample size limitations Uses sample size threshholds such that when areas fall below those threshholds values are borrowed from nearby areas. Uses a hierarchichacal modelling approach that shares information between areas in the same region. Thus all data is used, even with small sample sizes. This is a more sound method that avoids assumptions and uses all of the data.
Error propogation Error is propogated when variance estimates are available, but there is uncertainty associated with borrowing values from nearby areas, or the assumption of species compositions being identical in harvest and releases, are not dealt with. By breaking the assumption that species composition is equal between harvests and releases, uncertainty in the release estimates is more reflective of the fishery. Furthermore, the hyerarchichal approach more accurately captures uncertainy within and between areas within a region.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are overall harvest estimates from 1977- 1995 and release estimates from 1990-1995 that required some partitioning to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied to the pre-1996 values.

**Figure 0.**- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.

Figure 0.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.


SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook records are a census of guided harvests and releases.

SWHS Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides have been required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

**Figure 1.**- SWHS harvest (left) and release (right) estimates from guided trips (x-axis) versus repoted harvests from charter logbooks (y-axis).

Figure 1.- SWHS harvest (left) and release (right) estimates from guided trips (x-axis) versus repoted harvests from charter logbooks (y-axis).


A note on model development

To evaluate the discrepancy in apparent bias in harvest and release data, several models were explored to estimate releases during model development. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treated the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases. This tensions eventually highlighted the different release/retention probabilities between yelloweye and pelagics in the logbook data and prompted the current approach whereby that probability was calculated for the three main species complexes covered in the data: pelagics, yelloweye, and “other”. The methods described here follow the (\(LB_{fit}\)) formulation. Based on model behavior it is unlikely that the (\(LB_{cens}\)) model would work as there would not be enough data to estimate release probabilities. However, it may be worth running the (\(LB_{hyb}\)) approach as a sensitivity test at the very least.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish. In Southeast Alaska, the number of Demersal Shelf Rockfish (DSR, of which yelloweye are one species) and slope rockfish are also recorded.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta0_{(comp)ayu} + \frac{\beta1_{(comp)ayu}}{(1 + exp(\beta2_{(comp)ayu}*(y - \beta3_{(comp)ayu})))} + \beta4_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior. \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernible change in composition over the observed time period. \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was used for hindcasting.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested, \(pH_{(comp)ayu}\), by area, year, user group and species grouping. Because release data from the SWHS is for all rockfish and the release data from logbooks is only subdivided into pelagics, yelloweye and “other” (non-pelagic, non-yelloweye), we only estimated \(pH_{(comp)ayu}\) for those categories. Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases. For non-yelloweye DSR and Slope rockfish assemblages in Southeast Alaska \(R_{(DSR)ayu}\) and \(R_{(slope)ayu}\) were estimated from \(R_{(other)ayu}\) using the species composition data from the harvest, thus assuming that slope and DSR assemblages were caught and released at the same rates.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta0_{(pH)ayu} + \frac{\beta1_{(pH)ayuc}}{(1 + exp(\beta2_{(pH)ayuc}*(y - \beta3_{(pH)ayuc})))} + \beta4_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990. As with the compositional trends, \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernable change in harvest probability over the observed time period, \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was applied.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. As such, the release data are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), a second approaches was considered that loosened the assumption that logbook releases were a census. Results for this approach are not included in this document, but the methods are listed here for future reference and consideration. In a hybrid approach yelloweye and non-pelagic releases are regarded as a reliable census (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs was thus a proportion of the pelagic harvests

\[\begin{equation} x_{(black)ayu}~\sim~\textrm{Binomial}(P_{(black)ayu}, N_{ayu}^{pel}) \end{equation}\]

Yelloweye rockfish in Southcentral and Kodiak were modeled similarly as a proportion of the total number of non-pelagics such that

\[\begin{equation} x_{(yellow_{R2})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R2})ayu}, N_{ayu}^{nonpel}) \end{equation}\]

Southeast areas have several other non-pelagic groupings such that DSR and slope rockfish are a proportion of non-pelagics

\[\begin{equation} x_{(DSR)ayu}~\sim~\textrm{Binomial}(P_{(DSR)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

and

\[\begin{equation} x_{(slope)ayu}~\sim~\textrm{Binomial}(P_{(slope)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

with yelloweye in southeast a proportion of the DSR harvest

\[\begin{equation} x_{(yellow_{R1})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R1})ayu}, N_{ayu}^{DSR}) \end{equation}\].

Priors.

Priors range from uninformative to very informative or fixed. Priors for compositional logistic parameters are in Table 2 and proportion harvest logistic parameters are in Table 3. Until I figure out how to make a nice table in Rmarkdown, please refer to the attached spreadsheet and comp and harvp tabs.

Unresolved issues and outstanding questions:

  1. Reliability of unguided release estimates: These estimates have the least information feeding them and rely on the bias-corrected SWHS release estimates of all rockfish and the trends in release probability evident in the logbook data. The $ term that estimates the guided/unguided effect was given a very informative prior that tied the release probability of private anglers tightly to that of the charter fleet. The model is then trying to balance the three species complex estimates (pelagic, yelloweye and other) so that they sum to the total unguided releases estimated from the bias corrected SWHS data. For the most part this seems reasonable and appears to work, but there are certain areas where the estimates are “wonky”. Yelloweye releases in the Kodiak Northeast area in particular are significantly lower than for guided anglers with the same pattern evident in Cook Inlet to a lesser extent. Cook Inlet yelloweye numbers are very small, so this is a sample size issue with little consequence. The cause of the Kodiak northeast estimates is not clear to me at this point, but it must be a product of the bias corrected SWHS release estimates and how the model is divying up that estimate into the 3 species complexes. The results are also substantially different from the Howard methods and are much lower for black rockfish while disagreements for yelloweye are in both directions. Total rockfish releases more or less align with the total releases estimated with the Howard methods. Presumably, much of the discrepancy results from the substantial bias in release estimates from the SWHS. Interestingly, the logbook data indicates that the SWHS underestimates harvests but overestimates releases.

  2. Proportion guided estimates: There is not much data on this proportion prior to 2011 and it is not modeled with any sort of trend as was done for species composition and harvest proportions. With the exception of Cook Inlet and North Gulf Coast areas, there is little, if any, trend apparent in the data and perhaps this approach is the best available given the data available. However, if there are data sources somewhere that could inform this part of the model they could be incorporated.

  3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.

Results

**Figure X.**- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

**Figure 2.**- Total rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 2.- Total rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 3.**- Total rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

**Figure 4.**- Black rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


And black rockfish releases…

**Figure 5.**- Black rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Yellow rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Yellow rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 8.**- DSR rockfish (including yelloweye) harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 8.- DSR rockfish (including yelloweye) harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 9.**- DSR rockfish releases (including yelloweye) 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 9.- DSR rockfish releases (including yelloweye) 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 10.**- Slope rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 10.- Slope rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 11.**- Slope rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 11.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Model fit

Logbook residuals

**Figure 12.**- Residuals from logbook harvests

Figure 12.- Residuals from logbook harvests


SWHS residuals

**Figure 13.**- Residuals from SWHS harvests.

Figure 13.- Residuals from SWHS harvests.



**Figure 14.**- Residual of SWHS releases

Figure 14.- Residual of SWHS releases

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

**Figure 15.**- Mean percent of harvest by charter anglers.

Figure 15.- Mean percent of harvest by charter anglers.


When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although the model smooths out the changes and we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

**Figure 16.**- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

Figure 16.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.


**Figure 18.**- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 18.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 19.**- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 19.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 20.**- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

Figure 20.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.


## NULL


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SWHS bias

Figure 23 shows the mean estimate for SWHS bias in harvests and releases. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias. Bias in release estimates is substantial and whereas the SWHS appears to underestimate harvests, it appears to greatly overestimates releases by a factor of 2 or more in most areas as derived from logbook reported releases.

**Figure 23.**- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 23.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.


Our estimates of SWHS harvest bias track observations fairly well when he have guided harvest estimates. The estimates of release bias in the SWHS data track observed patterns to an extent, but appear to smooth these more volatile disagreements with the logbook data. Adam postulated in his initial start on this that some of this could be the result of the estimates of the proportion guided. This value was not modelled with a trend and thus applies a constant estimate when hindcasting. Data on these relationships could greatly improve this model.

**Figure 24.**- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 24.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 25 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

**Figure 25.**- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 25.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment. For the most part, P(black|pelagic) is relatively constant across areas, with the exception of Cook Inlet and NSEI in Southeast AK. It may be worth discussing whether the shifts in those areas is a result of improved or changing species identification rather than actual shift in the species composition of the catch.

**Figure 26.**- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 26.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(yelloweye|non-pelagic / yelloweye|DSR)

**Figure 27.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 27.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

**Figure 28.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

Figure 28.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

**Figure 30.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 30.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.



P(slope|non-pelagic & non-yellowye) For release estimates

**Figure 31.**- Annual estimates of the percent of the sport non-pelagic, non-yelloweye releases that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023.

Figure 31.- Annual estimates of the percent of the sport non-pelagic, non-yelloweye releases that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023.



Summary of unconverged parameters:

Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.
parameter n badRhat_avg
beta0_pelagic 3 1.950130
beta1_pelagic 3 1.942735
tau_beta0_pelagic 1 1.360244
mu_beta0_pelagic 1 1.274866
beta2_pelagic 2 1.253849
beta2_yellow 1 1.224501
parameter n badRhat_avg
beta2_pH 1 1.221732
beta1_black 1 1.166506
beta4_pelagic 1 1.143382
beta3_black 1 1.140671
beta2_black 1 1.124332
beta1_yellow 1 1.111078
Table 2. Summary of unconverged parameters by area
CI CSEO NSEI PWSI PWSO WKMA
beta0_pelagic 0 1 0 1 1 0
beta1_black 0 0 1 0 0 0
beta1_pelagic 0 1 0 1 1 0
beta1_yellow 1 0 0 0 0 0
beta2_black 0 0 1 0 0 0
beta2_pelagic 0 0 0 1 1 0
beta2_pH 0 0 0 0 0 1
beta2_yellow 0 0 0 0 1 0
beta3_black 0 0 1 0 0 0
beta4_pelagic 0 0 0 0 0 1
mu_beta0_pelagic 1 0 0 0 0 0
tau_beta0_pelagic 1 0 0 0 0 0

Parameter estimates:

Summary Table of Parameter Estimates
Parameter mean sd Lower_CI Median Upper_CI
mu_bc_H[1] -0.122 0.076 -0.259 -0.128 0.038
mu_bc_H[2] -0.098 0.044 -0.174 -0.102 0.003
mu_bc_H[3] -0.428 0.072 -0.563 -0.429 -0.279
mu_bc_H[4] -0.984 0.197 -1.386 -0.982 -0.615
mu_bc_H[5] 0.930 0.992 -0.143 0.737 3.253
mu_bc_H[6] -2.163 0.326 -2.786 -2.168 -1.483
mu_bc_H[7] -0.441 0.109 -0.659 -0.443 -0.232
mu_bc_H[8] 0.239 0.357 -0.358 0.209 1.060
mu_bc_H[9] -0.292 0.134 -0.554 -0.293 -0.032
mu_bc_H[10] -0.107 0.070 -0.238 -0.110 0.035
mu_bc_H[11] -0.123 0.037 -0.194 -0.123 -0.050
mu_bc_H[12] -0.253 0.105 -0.474 -0.249 -0.052
mu_bc_H[13] -0.135 0.078 -0.281 -0.137 0.020
mu_bc_H[14] -0.300 0.098 -0.501 -0.297 -0.114
mu_bc_H[15] -0.343 0.051 -0.437 -0.343 -0.243
mu_bc_H[16] -0.255 0.383 -0.937 -0.285 0.617
mu_bc_R[1] 1.355 0.149 1.057 1.356 1.650
mu_bc_R[2] 1.453 0.094 1.258 1.455 1.636
mu_bc_R[3] 1.401 0.142 1.124 1.400 1.676
mu_bc_R[4] 0.891 0.204 0.468 0.901 1.260
mu_bc_R[5] 1.169 0.475 0.255 1.177 2.078
mu_bc_R[6] -1.590 0.416 -2.416 -1.584 -0.782
mu_bc_R[7] 0.391 0.188 0.015 0.395 0.754
mu_bc_R[8] 0.558 0.198 0.157 0.565 0.920
mu_bc_R[9] 0.347 0.205 -0.115 0.363 0.700
mu_bc_R[10] 1.294 0.135 1.025 1.294 1.556
mu_bc_R[11] 1.035 0.097 0.844 1.034 1.226
mu_bc_R[12] 0.814 0.203 0.405 0.820 1.195
mu_bc_R[13] 1.028 0.103 0.824 1.027 1.225
mu_bc_R[14] 0.893 0.143 0.615 0.895 1.166
mu_bc_R[15] 0.785 0.107 0.568 0.788 0.990
mu_bc_R[16] 1.096 0.131 0.834 1.097 1.344
tau_pH[1] 5.212 0.441 4.372 5.190 6.131
tau_pH[2] 2.050 0.225 1.659 2.036 2.527
tau_pH[3] 2.266 0.224 1.839 2.256 2.722
beta0_pH[1,1] 0.568 0.171 0.231 0.571 0.900
beta0_pH[2,1] 1.370 0.179 1.012 1.369 1.713
beta0_pH[3,1] 1.426 0.190 1.008 1.436 1.770
beta0_pH[4,1] 1.571 0.218 1.094 1.582 1.945
beta0_pH[5,1] -0.866 0.274 -1.477 -0.842 -0.385
beta0_pH[6,1] -0.673 0.423 -1.684 -0.603 -0.044
beta0_pH[7,1] -0.490 0.441 -1.494 -0.463 0.346
beta0_pH[8,1] -0.672 0.273 -1.279 -0.642 -0.235
beta0_pH[9,1] -0.656 0.284 -1.293 -0.637 -0.154
beta0_pH[10,1] 0.232 0.204 -0.178 0.243 0.598
beta0_pH[11,1] -0.078 0.174 -0.424 -0.077 0.255
beta0_pH[12,1] 0.489 0.187 0.113 0.489 0.850
beta0_pH[13,1] 0.005 0.141 -0.278 0.006 0.288
beta0_pH[14,1] -0.318 0.163 -0.635 -0.316 -0.010
beta0_pH[15,1] -0.034 0.175 -0.393 -0.030 0.298
beta0_pH[16,1] -0.473 0.350 -1.318 -0.425 0.063
beta0_pH[1,2] 2.812 0.162 2.480 2.817 3.112
beta0_pH[2,2] 2.876 0.133 2.609 2.875 3.137
beta0_pH[3,2] 3.102 0.194 2.681 3.111 3.433
beta0_pH[4,2] 2.940 0.132 2.684 2.942 3.197
beta0_pH[5,2] 4.779 1.423 2.997 4.479 8.297
beta0_pH[6,2] 3.113 0.206 2.717 3.112 3.507
beta0_pH[7,2] 1.954 0.172 1.623 1.952 2.291
beta0_pH[8,2] 2.873 0.173 2.537 2.875 3.212
beta0_pH[9,2] 3.429 0.221 2.995 3.425 3.862
beta0_pH[10,2] 3.745 0.196 3.353 3.741 4.135
beta0_pH[11,2] -4.831 0.305 -5.457 -4.825 -4.267
beta0_pH[12,2] -4.774 0.388 -5.592 -4.763 -4.041
beta0_pH[13,2] -4.566 0.391 -5.310 -4.581 -3.776
beta0_pH[14,2] -5.584 0.485 -6.626 -5.549 -4.738
beta0_pH[15,2] -4.280 0.341 -4.921 -4.285 -3.593
beta0_pH[16,2] -4.867 0.382 -5.646 -4.857 -4.147
beta0_pH[1,3] 0.166 0.837 -2.033 0.315 1.219
beta0_pH[2,3] 2.192 0.155 1.885 2.192 2.497
beta0_pH[3,3] 2.525 0.147 2.235 2.525 2.815
beta0_pH[4,3] 2.962 0.156 2.650 2.961 3.264
beta0_pH[5,3] 1.399 1.639 -1.058 1.153 5.293
beta0_pH[6,3] -0.815 0.904 -2.207 -0.973 1.441
beta0_pH[7,3] -1.830 0.425 -2.692 -1.817 -1.032
beta0_pH[8,3] 0.283 0.189 -0.089 0.286 0.658
beta0_pH[9,3] -0.886 0.591 -2.536 -0.734 -0.141
beta0_pH[10,3] 0.389 0.417 -0.631 0.454 1.047
beta0_pH[11,3] -0.165 0.303 -0.729 -0.171 0.463
beta0_pH[12,3] -0.874 0.358 -1.613 -0.850 -0.244
beta0_pH[13,3] -0.128 0.292 -0.673 -0.135 0.460
beta0_pH[14,3] -0.278 0.255 -0.767 -0.286 0.231
beta0_pH[15,3] -0.687 0.287 -1.315 -0.675 -0.185
beta0_pH[16,3] -0.376 0.282 -0.918 -0.383 0.190
beta1_pH[1,1] 3.044 0.315 2.496 3.027 3.717
beta1_pH[2,1] 2.155 0.283 1.660 2.133 2.788
beta1_pH[3,1] 1.976 0.299 1.459 1.949 2.650
beta1_pH[4,1] 2.385 0.346 1.832 2.342 3.230
beta1_pH[5,1] 2.299 0.347 1.728 2.260 3.082
beta1_pH[6,1] 3.865 1.068 2.352 3.647 6.346
beta1_pH[7,1] 2.659 0.877 0.995 2.599 4.693
beta1_pH[8,1] 4.121 1.055 2.645 3.879 6.691
beta1_pH[9,1] 2.342 0.392 1.693 2.302 3.283
beta1_pH[10,1] 2.394 0.281 1.914 2.374 2.983
beta1_pH[11,1] 3.256 0.220 2.827 3.255 3.694
beta1_pH[12,1] 2.545 0.218 2.112 2.547 2.962
beta1_pH[13,1] 2.970 0.208 2.573 2.967 3.396
beta1_pH[14,1] 3.425 0.215 3.011 3.422 3.862
beta1_pH[15,1] 2.535 0.219 2.103 2.534 2.975
beta1_pH[16,1] 4.100 0.622 3.187 4.006 5.585
beta1_pH[1,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[2,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[3,2] 0.042 0.229 0.000 0.000 0.937
beta1_pH[4,2] 0.005 0.075 0.000 0.000 0.003
beta1_pH[5,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[6,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[7,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[8,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[9,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[10,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[11,2] 6.673 0.339 6.027 6.661 7.361
beta1_pH[12,2] 6.427 0.446 5.595 6.411 7.368
beta1_pH[13,2] 6.939 0.431 6.073 6.940 7.778
beta1_pH[14,2] 7.214 0.500 6.328 7.186 8.292
beta1_pH[15,2] 6.764 0.374 6.013 6.766 7.475
beta1_pH[16,2] 7.458 0.428 6.663 7.446 8.314
beta1_pH[1,3] 3.954 1.795 1.746 3.571 8.481
beta1_pH[2,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[3,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[4,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[5,3] 3.268 1.848 1.645 2.920 6.875
beta1_pH[6,3] 2.648 0.811 1.434 2.607 3.963
beta1_pH[7,3] 2.691 0.435 1.861 2.678 3.581
beta1_pH[8,3] 2.779 0.324 2.150 2.772 3.441
beta1_pH[9,3] 2.963 0.607 2.153 2.833 4.673
beta1_pH[10,3] 2.985 0.484 2.221 2.912 4.161
beta1_pH[11,3] 2.758 0.358 2.071 2.762 3.455
beta1_pH[12,3] 4.140 0.435 3.343 4.121 5.031
beta1_pH[13,3] 1.718 0.324 1.061 1.725 2.331
beta1_pH[14,3] 2.538 0.333 1.873 2.540 3.218
beta1_pH[15,3] 1.976 0.312 1.399 1.965 2.633
beta1_pH[16,3] 1.790 0.312 1.162 1.793 2.419
beta2_pH[1,1] 0.483 0.123 0.288 0.467 0.770
beta2_pH[2,1] 0.588 0.331 0.239 0.523 1.356
beta2_pH[3,1] 0.647 0.441 0.234 0.557 1.665
beta2_pH[4,1] 0.478 0.196 0.209 0.441 0.958
beta2_pH[5,1] 1.448 1.010 0.230 1.303 3.773
beta2_pH[6,1] 0.185 0.063 0.093 0.177 0.324
beta2_pH[7,1] 0.008 0.038 0.000 0.000 0.054
beta2_pH[8,1] 0.235 0.080 0.125 0.222 0.428
beta2_pH[9,1] 0.431 0.211 0.169 0.393 0.912
beta2_pH[10,1] 0.618 0.259 0.286 0.568 1.261
beta2_pH[11,1] 0.792 0.219 0.482 0.749 1.322
beta2_pH[12,1] 1.346 0.467 0.729 1.257 2.440
beta2_pH[13,1] 0.740 0.220 0.419 0.705 1.246
beta2_pH[14,1] 0.832 0.213 0.528 0.799 1.363
beta2_pH[15,1] 0.809 0.302 0.406 0.754 1.593
beta2_pH[16,1] 0.378 0.170 0.173 0.331 0.810
beta2_pH[1,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[2,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[3,2] -0.721 3.797 -8.166 -0.788 6.997
beta2_pH[4,2] -0.784 3.680 -8.441 -0.710 6.317
beta2_pH[5,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[6,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[7,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[8,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[9,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[10,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[11,2] -9.473 4.206 -20.123 -8.511 -4.117
beta2_pH[12,2] -8.094 4.933 -20.579 -7.288 -1.024
beta2_pH[13,2] -7.965 4.825 -19.913 -6.988 -1.772
beta2_pH[14,2] -8.538 4.571 -20.219 -7.444 -2.640
beta2_pH[15,2] -9.327 4.329 -20.353 -8.351 -3.755
beta2_pH[16,2] -9.510 4.320 -20.643 -8.588 -4.013
beta2_pH[1,3] 0.464 1.845 0.071 0.233 1.689
beta2_pH[2,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[3,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[4,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[5,3] 8.531 5.992 0.360 7.385 22.575
beta2_pH[6,3] 8.695 6.028 0.441 7.650 22.962
beta2_pH[7,3] 8.627 5.917 1.020 7.515 22.905
beta2_pH[8,3] 9.551 5.578 1.720 8.495 22.853
beta2_pH[9,3] 8.102 6.407 0.366 7.014 23.150
beta2_pH[10,3] 7.723 6.404 0.445 6.572 22.621
beta2_pH[11,3] -2.099 1.831 -7.117 -1.620 -0.612
beta2_pH[12,3] -2.233 1.702 -6.875 -1.772 -0.943
beta2_pH[13,3] -2.769 2.254 -9.385 -2.071 -0.814
beta2_pH[14,3] -2.664 2.134 -8.653 -2.015 -0.948
beta2_pH[15,3] -2.849 2.337 -9.595 -2.129 -1.015
beta2_pH[16,3] -2.852 2.298 -9.125 -2.144 -0.896
beta3_pH[1,1] 35.932 0.829 34.376 35.899 37.650
beta3_pH[2,1] 33.595 1.210 31.458 33.505 36.441
beta3_pH[3,1] 33.663 1.007 31.756 33.645 35.776
beta3_pH[4,1] 33.840 1.200 31.736 33.769 36.473
beta3_pH[5,1] 27.736 1.109 26.476 27.494 30.971
beta3_pH[6,1] 38.690 3.090 33.056 38.436 45.051
beta3_pH[7,1] 30.295 7.779 18.464 29.617 44.824
beta3_pH[8,1] 40.201 2.193 36.439 39.919 44.978
beta3_pH[9,1] 30.662 1.480 28.083 30.578 33.776
beta3_pH[10,1] 32.728 0.919 31.066 32.688 34.588
beta3_pH[11,1] 30.341 0.474 29.425 30.336 31.312
beta3_pH[12,1] 30.151 0.402 29.341 30.161 30.938
beta3_pH[13,1] 33.170 0.578 32.114 33.154 34.354
beta3_pH[14,1] 32.045 0.463 31.168 32.018 32.999
beta3_pH[15,1] 31.182 0.640 29.930 31.186 32.465
beta3_pH[16,1] 32.013 1.025 30.349 31.887 34.371
beta3_pH[1,2] 29.964 7.959 18.433 28.980 44.684
beta3_pH[2,2] 30.083 8.075 18.389 29.124 45.089
beta3_pH[3,2] 30.467 8.127 18.542 29.528 44.734
beta3_pH[4,2] 29.959 8.034 18.358 28.785 44.868
beta3_pH[5,2] 29.804 7.860 18.510 28.513 44.631
beta3_pH[6,2] 30.140 7.868 18.546 29.377 44.944
beta3_pH[7,2] 29.796 7.970 18.423 28.687 44.958
beta3_pH[8,2] 29.636 7.888 18.409 28.498 44.922
beta3_pH[9,2] 29.961 7.980 18.443 28.860 45.156
beta3_pH[10,2] 29.903 8.035 18.451 29.059 45.012
beta3_pH[11,2] 43.406 0.181 43.117 43.383 43.790
beta3_pH[12,2] 43.190 0.190 42.956 43.140 43.715
beta3_pH[13,2] 43.873 0.141 43.501 43.911 44.036
beta3_pH[14,2] 43.301 0.205 43.047 43.246 43.804
beta3_pH[15,2] 43.411 0.194 43.100 43.390 43.813
beta3_pH[16,2] 43.498 0.190 43.159 43.492 43.848
beta3_pH[1,3] 39.113 3.076 33.206 39.123 45.157
beta3_pH[2,3] 30.338 8.038 18.519 29.692 45.047
beta3_pH[3,3] 29.990 7.960 18.394 29.128 44.705
beta3_pH[4,3] 30.295 7.999 18.490 29.583 44.836
beta3_pH[5,3] 25.731 6.497 18.245 23.939 42.647
beta3_pH[6,3] 27.460 5.377 19.320 25.932 43.367
beta3_pH[7,3] 26.869 0.956 25.261 26.685 29.058
beta3_pH[8,3] 41.492 0.248 41.068 41.493 41.935
beta3_pH[9,3] 32.981 1.487 28.494 33.442 34.201
beta3_pH[10,3] 35.697 0.880 33.298 35.976 36.808
beta3_pH[11,3] 41.804 0.765 40.234 41.843 43.196
beta3_pH[12,3] 41.734 0.390 40.987 41.747 42.468
beta3_pH[13,3] 42.733 0.821 41.181 42.742 44.476
beta3_pH[14,3] 41.103 0.552 39.908 41.130 42.110
beta3_pH[15,3] 42.558 0.637 41.133 42.611 43.683
beta3_pH[16,3] 42.875 0.750 41.145 42.967 44.091
beta0_pelagic[1] 2.208 0.134 1.936 2.209 2.463
beta0_pelagic[2] 1.514 0.129 1.265 1.513 1.766
beta0_pelagic[3] -0.533 1.677 -5.152 0.164 0.950
beta0_pelagic[4] 0.096 1.191 -2.734 0.647 1.191
beta0_pelagic[5] 1.199 0.255 0.680 1.200 1.707
beta0_pelagic[6] 1.469 0.268 0.911 1.486 1.967
beta0_pelagic[7] 1.700 0.240 1.289 1.672 2.256
beta0_pelagic[8] 1.764 0.205 1.374 1.759 2.204
beta0_pelagic[9] 2.501 0.313 1.896 2.514 3.062
beta0_pelagic[10] 2.540 0.199 2.117 2.547 2.910
beta0_pelagic[11] 0.163 0.496 -1.099 0.358 0.761
beta0_pelagic[12] 1.680 0.147 1.401 1.676 1.962
beta0_pelagic[13] 0.300 0.220 -0.170 0.319 0.674
beta0_pelagic[14] -0.101 0.313 -0.854 -0.063 0.388
beta0_pelagic[15] -0.261 0.139 -0.534 -0.259 0.017
beta0_pelagic[16] 0.329 0.247 -0.329 0.373 0.676
beta1_pelagic[1] 0.000 0.000 0.000 0.000 0.000
beta1_pelagic[2] 0.000 0.000 0.000 0.000 0.000
beta1_pelagic[3] 2.365 3.122 0.000 1.069 11.499
beta1_pelagic[4] 1.591 2.280 0.000 0.545 7.275
beta1_pelagic[5] -0.087 0.311 -0.714 -0.092 0.531
beta1_pelagic[6] -0.091 0.449 -0.862 -0.131 0.752
beta1_pelagic[7] -0.021 0.356 -0.710 -0.017 0.655
beta1_pelagic[8] -0.006 0.282 -0.532 -0.005 0.548
beta1_pelagic[9] 0.184 0.485 -0.785 0.290 0.944
beta1_pelagic[10] 0.057 0.257 -0.454 0.055 0.565
beta1_pelagic[11] 3.400 1.150 2.054 2.977 6.168
beta1_pelagic[12] 2.773 0.320 2.164 2.772 3.410
beta1_pelagic[13] 2.959 0.752 1.768 2.871 4.798
beta1_pelagic[14] 4.294 1.065 2.740 4.098 6.586
beta1_pelagic[15] 2.899 0.272 2.374 2.894 3.438
beta1_pelagic[16] 3.460 0.747 2.671 3.263 5.990
beta2_pelagic[1] 0.000 0.000 0.000 0.000 0.000
beta2_pelagic[2] 0.000 0.000 0.000 0.000 0.000
beta2_pelagic[3] 0.259 1.874 0.000 0.032 1.163
beta2_pelagic[4] 0.625 3.085 0.000 0.024 5.486
beta2_pelagic[5] -0.010 0.662 -1.437 -0.002 1.353
beta2_pelagic[6] -0.099 0.708 -1.541 -0.140 1.328
beta2_pelagic[7] 0.014 0.698 -1.458 0.013 1.494
beta2_pelagic[8] 0.010 0.658 -1.388 0.010 1.393
beta2_pelagic[9] 0.180 0.700 -1.316 0.241 1.534
beta2_pelagic[10] 0.011 0.642 -1.361 0.012 1.344
beta2_pelagic[11] 2.862 4.752 0.113 0.629 16.569
beta2_pelagic[12] 6.594 5.513 1.080 4.883 21.040
beta2_pelagic[13] 0.938 1.892 0.181 0.466 5.648
beta2_pelagic[14] 0.348 0.317 0.153 0.294 0.817
beta2_pelagic[15] 6.712 5.308 1.317 5.181 21.585
beta2_pelagic[16] 5.208 5.536 0.212 3.767 20.289
beta3_pelagic[1] 29.988 8.033 18.438 29.006 44.882
beta3_pelagic[2] 29.746 7.909 18.509 28.746 44.781
beta3_pelagic[3] 30.032 7.419 18.515 29.362 44.595
beta3_pelagic[4] 29.311 7.404 18.723 27.274 44.576
beta3_pelagic[5] 29.683 8.131 18.478 28.350 45.150
beta3_pelagic[6] 31.863 6.779 18.982 31.985 44.319
beta3_pelagic[7] 29.060 7.180 18.526 28.253 44.562
beta3_pelagic[8] 29.265 7.954 18.437 27.867 44.914
beta3_pelagic[9] 30.742 6.168 19.095 30.758 42.843
beta3_pelagic[10] 29.658 8.113 18.394 28.334 45.039
beta3_pelagic[11] 42.539 1.906 36.817 43.072 45.412
beta3_pelagic[12] 43.469 0.283 43.004 43.454 43.983
beta3_pelagic[13] 42.858 1.324 40.276 42.842 45.625
beta3_pelagic[14] 42.327 1.651 39.011 42.319 45.513
beta3_pelagic[15] 43.189 0.272 42.538 43.190 43.693
beta3_pelagic[16] 43.108 0.708 41.475 43.208 44.387
mu_beta0_pelagic[1] 0.812 1.122 -1.901 1.020 2.671
mu_beta0_pelagic[2] 1.837 0.370 1.047 1.836 2.549
mu_beta0_pelagic[3] 0.361 0.458 -0.598 0.372 1.247
tau_beta0_pelagic[1] 0.938 1.297 0.048 0.418 4.754
tau_beta0_pelagic[2] 2.702 2.795 0.273 1.968 9.165
tau_beta0_pelagic[3] 1.558 1.220 0.183 1.236 4.851
beta0_yellow[1] -0.531 0.194 -0.972 -0.516 -0.203
beta0_yellow[2] 0.481 0.195 0.083 0.494 0.793
beta0_yellow[3] -0.329 0.209 -0.760 -0.316 0.015
beta0_yellow[4] 0.808 0.323 -0.060 0.867 1.201
beta0_yellow[5] -0.330 0.361 -1.037 -0.329 0.397
beta0_yellow[6] 1.137 0.169 0.797 1.136 1.476
beta0_yellow[7] 1.069 0.159 0.757 1.071 1.373
beta0_yellow[8] 1.012 0.157 0.704 1.011 1.320
beta0_yellow[9] 0.669 0.157 0.362 0.665 0.976
beta0_yellow[10] 0.578 0.145 0.297 0.577 0.864
beta0_yellow[11] -1.974 0.437 -2.857 -1.977 -1.134
beta0_yellow[12] -3.698 0.438 -4.642 -3.669 -2.933
beta0_yellow[13] -3.720 0.456 -4.677 -3.686 -2.919
beta0_yellow[14] -2.066 0.613 -3.085 -2.122 -0.421
beta0_yellow[15] -2.863 0.430 -3.765 -2.840 -2.079
beta0_yellow[16] -2.448 0.480 -3.396 -2.462 -1.502
beta1_yellow[1] 1.019 2.120 0.015 0.721 3.616
beta1_yellow[2] 1.125 0.469 0.595 1.049 2.417
beta1_yellow[3] 0.747 0.367 0.272 0.710 1.422
beta1_yellow[4] 1.468 0.837 0.653 1.234 4.185
beta1_yellow[5] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[6] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[7] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[8] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[9] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[10] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[11] 2.124 0.431 1.276 2.121 2.969
beta1_yellow[12] 2.497 0.451 1.695 2.468 3.447
beta1_yellow[13] 2.832 0.458 2.031 2.798 3.789
beta1_yellow[14] 2.171 0.564 0.840 2.197 3.190
beta1_yellow[15] 2.108 0.432 1.307 2.090 3.032
beta1_yellow[16] 2.202 0.478 1.256 2.212 3.141
beta2_yellow[1] -3.358 2.968 -10.789 -2.486 -0.062
beta2_yellow[2] -3.318 2.972 -11.149 -2.497 -0.140
beta2_yellow[3] -3.281 3.158 -11.942 -2.301 -0.120
beta2_yellow[4] -2.485 2.918 -10.434 -1.287 -0.090
beta2_yellow[5] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[6] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[7] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[8] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[9] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[10] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[11] -4.547 2.629 -11.335 -3.942 -1.088
beta2_yellow[12] -4.887 2.494 -10.988 -4.421 -1.308
beta2_yellow[13] -4.871 2.240 -10.205 -4.524 -1.658
beta2_yellow[14] -4.832 2.822 -11.869 -4.420 -0.221
beta2_yellow[15] -4.418 2.644 -11.017 -3.820 -1.050
beta2_yellow[16] -4.915 2.642 -11.709 -4.399 -1.378
beta3_yellow[1] 25.473 7.015 18.257 22.375 43.899
beta3_yellow[2] 29.043 2.104 23.618 28.870 33.117
beta3_yellow[3] 32.850 3.245 24.553 32.825 39.928
beta3_yellow[4] 28.966 3.784 20.388 28.112 36.758
beta3_yellow[5] 29.730 7.857 18.512 28.715 44.721
beta3_yellow[6] 29.913 7.891 18.518 29.018 44.895
beta3_yellow[7] 30.052 8.048 18.510 29.196 44.967
beta3_yellow[8] 29.892 8.056 18.444 28.778 44.770
beta3_yellow[9] 30.048 7.802 18.481 29.378 44.821
beta3_yellow[10] 30.166 7.865 18.569 29.365 44.943
beta3_yellow[11] 45.311 0.515 44.036 45.405 45.974
beta3_yellow[12] 43.294 0.424 42.540 43.277 44.045
beta3_yellow[13] 44.887 0.389 44.035 44.957 45.533
beta3_yellow[14] 43.790 2.238 34.623 44.187 45.845
beta3_yellow[15] 45.163 0.533 44.185 45.137 45.971
beta3_yellow[16] 44.577 0.677 43.395 44.570 45.835
mu_beta0_yellow[1] 0.088 0.546 -1.090 0.103 1.182
mu_beta0_yellow[2] 0.642 0.358 -0.186 0.667 1.307
mu_beta0_yellow[3] -2.435 0.653 -3.450 -2.529 -0.772
tau_beta0_yellow[1] 1.926 2.871 0.092 1.168 8.102
tau_beta0_yellow[2] 3.148 3.622 0.285 2.125 12.162
tau_beta0_yellow[3] 1.436 2.181 0.096 0.906 5.886
beta0_black[1] -0.077 0.162 -0.401 -0.078 0.244
beta0_black[2] 1.916 0.128 1.671 1.916 2.168
beta0_black[3] 1.322 0.138 1.052 1.322 1.587
beta0_black[4] 2.428 0.138 2.152 2.428 2.701
beta0_black[5] 1.543 2.009 -2.935 1.659 5.517
beta0_black[6] 1.597 1.972 -2.984 1.677 5.386
beta0_black[7] 1.585 2.013 -2.963 1.642 5.734
beta0_black[8] 1.298 0.227 0.865 1.294 1.749
beta0_black[9] 2.450 0.253 1.946 2.457 2.942
beta0_black[10] 1.480 0.136 1.217 1.480 1.746
beta0_black[11] 3.484 0.158 3.175 3.484 3.785
beta0_black[12] 4.864 0.179 4.500 4.870 5.214
beta0_black[13] -0.167 0.339 -0.888 -0.130 0.311
beta0_black[14] 2.859 0.160 2.539 2.856 3.173
beta0_black[15] 1.291 0.156 0.989 1.288 1.599
beta0_black[16] 4.271 0.160 3.969 4.273 4.573
beta2_black[1] 7.801 10.049 0.477 3.488 40.188
beta2_black[2] 0.000 0.000 0.000 0.000 0.000
beta2_black[3] 0.000 0.000 0.000 0.000 0.000
beta2_black[4] 0.000 0.000 0.000 0.000 0.000
beta2_black[5] 0.000 0.000 0.000 0.000 0.000
beta2_black[6] 0.000 0.000 0.000 0.000 0.000
beta2_black[7] 0.000 0.000 0.000 0.000 0.000
beta2_black[8] 0.000 0.000 0.000 0.000 0.000
beta2_black[9] 0.000 0.000 0.000 0.000 0.000
beta2_black[10] 0.000 0.000 0.000 0.000 0.000
beta2_black[11] 0.000 0.000 0.000 0.000 0.000
beta2_black[12] 0.000 0.000 0.000 0.000 0.000
beta2_black[13] -1.733 1.474 -5.855 -1.253 -0.168
beta2_black[14] 0.000 0.000 0.000 0.000 0.000
beta2_black[15] 0.000 0.000 0.000 0.000 0.000
beta2_black[16] 0.000 0.000 0.000 0.000 0.000
beta3_black[1] 41.799 1.043 39.833 41.970 43.246
beta3_black[2] 25.000 0.000 25.000 25.000 25.000
beta3_black[3] 25.000 0.000 25.000 25.000 25.000
beta3_black[4] 25.000 0.000 25.000 25.000 25.000
beta3_black[5] 25.000 0.000 25.000 25.000 25.000
beta3_black[6] 25.000 0.000 25.000 25.000 25.000
beta3_black[7] 25.000 0.000 25.000 25.000 25.000
beta3_black[8] 25.000 0.000 25.000 25.000 25.000
beta3_black[9] 25.000 0.000 25.000 25.000 25.000
beta3_black[10] 25.000 0.000 25.000 25.000 25.000
beta3_black[11] 25.000 0.000 25.000 25.000 25.000
beta3_black[12] 25.000 0.000 25.000 25.000 25.000
beta3_black[13] 38.908 2.081 34.679 39.252 40.647
beta3_black[14] 25.000 0.000 25.000 25.000 25.000
beta3_black[15] 25.000 0.000 25.000 25.000 25.000
beta3_black[16] 25.000 0.000 25.000 25.000 25.000
beta4_black[1] -0.262 0.197 -0.650 -0.257 0.104
beta4_black[2] 0.241 0.184 -0.113 0.243 0.606
beta4_black[3] -0.935 0.195 -1.303 -0.937 -0.551
beta4_black[4] 0.424 0.226 -0.022 0.420 0.866
beta4_black[5] 0.236 2.378 -4.514 0.147 5.039
beta4_black[6] 0.215 2.425 -4.632 0.166 4.942
beta4_black[7] 0.249 2.424 -4.340 0.166 5.104
beta4_black[8] -0.707 0.371 -1.451 -0.705 0.012
beta4_black[9] 1.484 1.052 -0.190 1.354 3.971
beta4_black[10] 0.020 0.190 -0.360 0.022 0.386
beta4_black[11] -0.691 0.214 -1.108 -0.690 -0.272
beta4_black[12] 0.173 0.329 -0.449 0.158 0.814
beta4_black[13] -1.180 0.232 -1.637 -1.179 -0.734
beta4_black[14] -0.188 0.239 -0.656 -0.190 0.287
beta4_black[15] -0.886 0.216 -1.316 -0.883 -0.472
beta4_black[16] -0.593 0.228 -1.023 -0.592 -0.135
mu_beta0_black[1] 1.301 0.914 -0.715 1.322 3.152
mu_beta0_black[2] 1.593 0.920 -0.566 1.671 3.275
mu_beta0_black[3] 2.530 0.980 0.457 2.578 4.393
tau_beta0_black[1] 0.646 0.624 0.058 0.455 2.359
tau_beta0_black[2] 1.867 3.281 0.055 0.823 10.305
tau_beta0_black[3] 0.235 0.156 0.049 0.201 0.649
beta0_dsr[11] -2.904 0.298 -3.490 -2.912 -2.312
beta0_dsr[12] 4.571 0.282 4.036 4.566 5.139
beta0_dsr[13] -1.371 0.365 -2.052 -1.355 -0.757
beta0_dsr[14] -3.662 0.528 -4.736 -3.656 -2.612
beta0_dsr[15] -1.944 0.291 -2.517 -1.940 -1.382
beta0_dsr[16] -2.993 0.374 -3.738 -2.990 -2.268
beta1_dsr[11] 4.838 0.310 4.241 4.845 5.447
beta1_dsr[12] 7.067 12.251 2.300 5.046 22.328
beta1_dsr[13] 2.897 0.439 2.254 2.861 3.650
beta1_dsr[14] 6.329 0.552 5.251 6.325 7.431
beta1_dsr[15] 3.347 0.295 2.784 3.346 3.932
beta1_dsr[16] 5.813 0.393 5.045 5.808 6.582
beta2_dsr[11] -8.278 2.423 -14.151 -7.899 -4.667
beta2_dsr[12] -7.065 2.719 -13.123 -6.848 -2.315
beta2_dsr[13] -6.432 2.833 -12.484 -6.283 -0.564
beta2_dsr[14] -6.077 2.714 -11.976 -5.883 -1.809
beta2_dsr[15] -7.738 2.446 -13.494 -7.420 -3.854
beta2_dsr[16] -7.869 2.393 -13.291 -7.504 -4.145
beta3_dsr[11] 43.485 0.150 43.207 43.481 43.775
beta3_dsr[12] 33.950 0.772 32.065 34.121 34.818
beta3_dsr[13] 43.242 0.372 42.733 43.195 43.883
beta3_dsr[14] 43.352 0.234 43.078 43.284 43.937
beta3_dsr[15] 43.512 0.187 43.170 43.512 43.851
beta3_dsr[16] 43.443 0.159 43.173 43.426 43.766
beta4_dsr[11] 0.592 0.226 0.159 0.593 1.047
beta4_dsr[12] 0.239 0.442 -0.634 0.223 1.132
beta4_dsr[13] -0.165 0.222 -0.601 -0.161 0.261
beta4_dsr[14] 0.144 0.253 -0.365 0.146 0.636
beta4_dsr[15] 0.722 0.213 0.315 0.723 1.148
beta4_dsr[16] 0.146 0.228 -0.307 0.153 0.584
beta0_slope[11] -1.846 0.147 -2.138 -1.845 -1.560
beta0_slope[12] -4.470 0.264 -5.010 -4.462 -3.978
beta0_slope[13] -1.333 0.179 -1.710 -1.320 -1.031
beta0_slope[14] -2.670 0.167 -2.991 -2.675 -2.340
beta0_slope[15] -1.340 0.147 -1.630 -1.342 -1.051
beta0_slope[16] -2.732 0.158 -3.035 -2.733 -2.427
beta1_slope[11] 4.488 0.222 4.059 4.492 4.922
beta1_slope[12] 3.971 0.452 3.114 3.965 4.897
beta1_slope[13] 2.701 0.413 2.196 2.637 3.885
beta1_slope[14] 6.311 0.416 5.534 6.297 7.151
beta1_slope[15] 3.004 0.211 2.583 3.010 3.417
beta1_slope[16] 5.284 0.279 4.749 5.286 5.833
beta2_slope[11] 8.637 2.293 5.100 8.283 13.805
beta2_slope[12] 6.676 2.977 1.181 6.647 12.647
beta2_slope[13] 5.399 2.985 0.433 5.316 11.622
beta2_slope[14] 6.467 2.503 2.292 6.328 11.959
beta2_slope[15] 8.201 2.333 4.521 7.848 13.650
beta2_slope[16] 7.725 2.286 4.153 7.397 13.148
beta3_slope[11] 43.461 0.135 43.220 43.455 43.732
beta3_slope[12] 43.350 0.283 42.857 43.309 43.906
beta3_slope[13] 43.453 0.380 42.917 43.395 44.037
beta3_slope[14] 43.263 0.134 43.092 43.234 43.615
beta3_slope[15] 43.495 0.160 43.197 43.493 43.797
beta3_slope[16] 43.375 0.143 43.153 43.355 43.696
beta4_slope[11] -0.732 0.161 -1.048 -0.735 -0.414
beta4_slope[12] -1.149 0.455 -2.120 -1.120 -0.356
beta4_slope[13] 0.084 0.166 -0.244 0.084 0.401
beta4_slope[14] -0.090 0.196 -0.471 -0.091 0.299
beta4_slope[15] -0.769 0.162 -1.089 -0.770 -0.450
beta4_slope[16] -0.162 0.178 -0.516 -0.165 0.180
sigma_H[1] 0.204 0.056 0.102 0.201 0.326
sigma_H[2] 0.171 0.030 0.119 0.169 0.232
sigma_H[3] 0.196 0.042 0.121 0.194 0.284
sigma_H[4] 0.423 0.076 0.300 0.414 0.601
sigma_H[5] 0.998 0.209 0.621 0.986 1.425
sigma_H[6] 0.382 0.200 0.032 0.378 0.786
sigma_H[7] 0.316 0.067 0.212 0.307 0.473
sigma_H[8] 0.417 0.095 0.276 0.405 0.614
sigma_H[9] 0.527 0.126 0.328 0.510 0.803
sigma_H[10] 0.216 0.042 0.144 0.212 0.302
sigma_H[11] 0.278 0.046 0.201 0.274 0.383
sigma_H[12] 0.433 0.163 0.207 0.405 0.774
sigma_H[13] 0.214 0.038 0.150 0.210 0.297
sigma_H[14] 0.506 0.093 0.343 0.500 0.702
sigma_H[15] 0.247 0.041 0.178 0.243 0.342
sigma_H[16] 0.224 0.044 0.153 0.220 0.323
lambda_H[1] 3.154 4.122 0.174 1.832 14.390
lambda_H[2] 8.184 7.768 0.780 5.920 28.134
lambda_H[3] 6.394 10.072 0.268 3.157 32.885
lambda_H[4] 0.006 0.004 0.001 0.005 0.018
lambda_H[5] 3.955 7.662 0.036 1.104 26.352
lambda_H[6] 8.154 15.396 0.008 1.000 52.839
lambda_H[7] 0.011 0.008 0.002 0.009 0.033
lambda_H[8] 8.399 10.433 0.140 4.935 37.296
lambda_H[9] 0.015 0.010 0.003 0.013 0.040
lambda_H[10] 0.301 0.462 0.034 0.200 1.068
lambda_H[11] 0.261 0.390 0.011 0.133 1.215
lambda_H[12] 4.879 6.261 0.188 2.798 23.557
lambda_H[13] 3.474 3.100 0.242 2.573 11.546
lambda_H[14] 3.305 4.269 0.221 2.045 14.451
lambda_H[15] 0.028 0.144 0.003 0.016 0.107
lambda_H[16] 0.808 1.151 0.043 0.424 4.112
mu_lambda_H[1] 4.317 1.894 1.219 4.176 8.454
mu_lambda_H[2] 3.917 1.952 0.638 3.790 8.119
mu_lambda_H[3] 3.562 1.919 0.767 3.253 7.961
sigma_lambda_H[1] 8.596 4.326 1.967 7.976 18.292
sigma_lambda_H[2] 8.545 4.689 1.060 8.039 18.534
sigma_lambda_H[3] 6.439 4.158 0.983 5.510 16.818
beta_H[1,1] 6.923 1.044 4.405 7.097 8.560
beta_H[2,1] 9.874 0.492 8.802 9.895 10.786
beta_H[3,1] 7.983 0.802 6.077 8.081 9.259
beta_H[4,1] 9.607 7.862 -6.715 9.786 24.371
beta_H[5,1] 0.164 2.216 -4.448 0.362 3.888
beta_H[6,1] 3.236 3.976 -6.670 4.653 7.828
beta_H[7,1] -0.726 6.231 -14.001 -0.265 10.658
beta_H[8,1] 1.384 4.113 -2.337 1.249 3.514
beta_H[9,1] 12.998 5.503 1.822 13.061 23.741
beta_H[10,1] 7.108 1.719 3.545 7.181 10.411
beta_H[11,1] 5.106 3.558 -2.933 5.889 9.946
beta_H[12,1] 2.603 1.032 0.805 2.517 4.770
beta_H[13,1] 9.042 0.967 7.166 9.131 10.483
beta_H[14,1] 2.212 1.041 0.134 2.227 4.272
beta_H[15,1] -6.021 3.843 -12.985 -6.317 2.503
beta_H[16,1] 3.495 2.698 -0.804 3.113 9.843
beta_H[1,2] 7.905 0.246 7.377 7.912 8.369
beta_H[2,2] 10.027 0.135 9.762 10.028 10.287
beta_H[3,2] 8.952 0.200 8.565 8.949 9.344
beta_H[4,2] 3.559 1.503 0.712 3.501 6.642
beta_H[5,2] 1.952 0.922 0.131 1.960 3.704
beta_H[6,2] 5.729 1.091 3.144 5.917 7.345
beta_H[7,2] 2.993 1.192 0.894 2.940 5.534
beta_H[8,2] 3.027 1.094 1.415 3.154 4.228
beta_H[9,2] 3.510 1.105 1.425 3.474 5.834
beta_H[10,2] 8.208 0.348 7.465 8.217 8.841
beta_H[11,2] 9.771 0.633 8.835 9.649 11.208
beta_H[12,2] 3.945 0.370 3.269 3.929 4.720
beta_H[13,2] 9.125 0.259 8.681 9.116 9.626
beta_H[14,2] 4.016 0.352 3.316 4.013 4.720
beta_H[15,2] 11.351 0.693 9.859 11.381 12.623
beta_H[16,2] 4.510 0.803 2.970 4.507 6.101
beta_H[1,3] 8.449 0.248 8.001 8.431 8.957
beta_H[2,3] 10.069 0.115 9.837 10.069 10.302
beta_H[3,3] 9.611 0.164 9.286 9.607 9.951
beta_H[4,3] -2.538 0.888 -4.276 -2.533 -0.803
beta_H[5,3] 3.826 0.610 2.597 3.836 4.984
beta_H[6,3] 8.004 1.200 6.348 7.609 10.659
beta_H[7,3] -3.120 0.696 -4.518 -3.110 -1.761
beta_H[8,3] 5.242 0.477 4.679 5.185 6.074
beta_H[9,3] -2.854 0.745 -4.358 -2.802 -1.447
beta_H[10,3] 8.677 0.278 8.146 8.678 9.225
beta_H[11,3] 8.535 0.289 7.908 8.557 9.046
beta_H[12,3] 5.255 0.319 4.504 5.301 5.766
beta_H[13,3] 8.842 0.177 8.479 8.845 9.171
beta_H[14,3] 5.715 0.278 5.090 5.734 6.212
beta_H[15,3] 10.369 0.320 9.743 10.364 10.999
beta_H[16,3] 6.229 0.600 4.935 6.293 7.201
beta_H[1,4] 8.252 0.184 7.854 8.266 8.576
beta_H[2,4] 10.133 0.119 9.886 10.140 10.347
beta_H[3,4] 10.105 0.166 9.725 10.122 10.383
beta_H[4,4] 11.804 0.453 10.890 11.808 12.669
beta_H[5,4] 5.471 0.737 4.288 5.394 7.106
beta_H[6,4] 7.069 0.930 4.902 7.353 8.336
beta_H[7,4] 8.317 0.364 7.579 8.327 9.014
beta_H[8,4] 6.711 0.245 6.256 6.719 7.134
beta_H[9,4] 7.204 0.473 6.297 7.194 8.150
beta_H[10,4] 7.760 0.234 7.314 7.753 8.217
beta_H[11,4] 9.388 0.199 9.013 9.388 9.792
beta_H[12,4] 7.142 0.210 6.734 7.140 7.565
beta_H[13,4] 9.050 0.144 8.749 9.053 9.333
beta_H[14,4] 7.730 0.219 7.327 7.727 8.178
beta_H[15,4] 9.470 0.241 9.011 9.470 9.952
beta_H[16,4] 9.338 0.238 8.908 9.328 9.844
beta_H[1,5] 8.984 0.145 8.682 8.990 9.265
beta_H[2,5] 10.786 0.093 10.611 10.783 10.978
beta_H[3,5] 10.915 0.173 10.614 10.906 11.269
beta_H[4,5] 8.379 0.467 7.507 8.369 9.352
beta_H[5,5] 5.427 0.587 4.069 5.478 6.438
beta_H[6,5] 8.792 0.623 7.914 8.655 10.291
beta_H[7,5] 6.744 0.355 6.065 6.739 7.467
beta_H[8,5] 8.216 0.206 7.864 8.203 8.616
beta_H[9,5] 8.213 0.481 7.267 8.225 9.152
beta_H[10,5] 10.085 0.225 9.633 10.091 10.524
beta_H[11,5] 11.509 0.228 11.053 11.508 11.952
beta_H[12,5] 8.482 0.197 8.091 8.476 8.902
beta_H[13,5] 10.012 0.132 9.752 10.008 10.268
beta_H[14,5] 9.202 0.234 8.786 9.190 9.698
beta_H[15,5] 11.162 0.252 10.665 11.169 11.640
beta_H[16,5] 9.921 0.176 9.563 9.929 10.247
beta_H[1,6] 10.184 0.184 9.861 10.173 10.600
beta_H[2,6] 11.511 0.106 11.293 11.511 11.719
beta_H[3,6] 10.810 0.164 10.456 10.820 11.100
beta_H[4,6] 12.893 0.826 11.204 12.909 14.503
beta_H[5,6] 5.886 0.597 4.774 5.877 7.066
beta_H[6,6] 8.763 0.692 6.976 8.893 9.749
beta_H[7,6] 9.881 0.597 8.708 9.891 11.008
beta_H[8,6] 9.527 0.275 9.040 9.539 9.980
beta_H[9,6] 8.452 0.802 6.887 8.436 10.083
beta_H[10,6] 9.515 0.314 8.825 9.540 10.073
beta_H[11,6] 10.813 0.354 10.060 10.840 11.439
beta_H[12,6] 9.367 0.249 8.903 9.357 9.910
beta_H[13,6] 11.052 0.171 10.760 11.039 11.416
beta_H[14,6] 9.820 0.292 9.243 9.823 10.370
beta_H[15,6] 10.843 0.452 9.977 10.835 11.763
beta_H[16,6] 10.527 0.242 10.013 10.543 10.976
beta_H[1,7] 10.883 0.845 8.870 10.983 12.248
beta_H[2,7] 12.203 0.434 11.310 12.213 13.014
beta_H[3,7] 10.548 0.677 9.077 10.612 11.669
beta_H[4,7] 2.387 4.216 -5.825 2.293 10.768
beta_H[5,7] 6.454 1.820 3.064 6.402 10.406
beta_H[6,7] 9.653 2.490 4.960 9.540 16.125
beta_H[7,7] 10.537 2.951 4.859 10.480 16.542
beta_H[8,7] 10.951 1.012 9.417 10.924 12.453
beta_H[9,7] 4.531 4.113 -4.058 4.562 12.624
beta_H[10,7] 9.799 1.424 7.140 9.720 12.925
beta_H[11,7] 10.974 1.746 7.777 10.820 14.728
beta_H[12,7] 10.000 0.929 7.971 10.078 11.602
beta_H[13,7] 11.636 0.777 9.828 11.753 12.795
beta_H[14,7] 10.362 0.970 8.167 10.430 12.081
beta_H[15,7] 11.999 2.277 7.393 12.008 16.345
beta_H[16,7] 12.311 1.266 10.270 12.166 15.207
beta0_H[1] 8.765 13.053 -17.938 8.750 33.753
beta0_H[2] 10.619 6.443 -2.476 10.605 24.151
beta0_H[3] 9.642 9.955 -11.127 9.905 29.020
beta0_H[4] 4.774 179.501 -344.066 6.311 365.548
beta0_H[5] 4.192 22.734 -40.674 4.287 47.819
beta0_H[6] 7.367 49.538 -93.381 7.396 117.678
beta0_H[7] 7.004 147.456 -278.602 5.857 302.916
beta0_H[8] 5.812 41.000 -14.710 6.392 27.311
beta0_H[9] 4.397 121.418 -243.519 3.700 239.939
beta0_H[10] 8.975 33.054 -58.024 8.397 78.144
beta0_H[11] 11.059 49.483 -91.717 10.857 111.482
beta0_H[12] 6.754 12.712 -15.970 6.618 29.031
beta0_H[13] 9.648 11.882 -11.830 9.837 28.485
beta0_H[14] 7.032 11.941 -16.293 7.077 30.069
beta0_H[15] 10.898 106.466 -208.781 10.976 231.295
beta0_H[16] 8.332 26.432 -46.546 8.068 61.317